已知椭圆E的中心在坐标原点O，经过两点A(1，
（1）求椭圆E的标准方程； （2）若点P是圆C上的一个动点，求
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（1）设椭圆E的标准方程为mx2+ny2=1（m＞0，n＞0，且m≠n）．
因为A(1，
)，B(-2，2 5 5
)在椭圆E上，所以5 5 m+
n=14 5 4m+
n=11 5
解得m=
，n=1，满足条件1 5
所以所求椭圆E的标准方程为
+y2=1.x2 5
（2）由（1）知椭圆的短半轴长为1，所以圆心坐标为（2，0），半径r=1，
故圆C的方程为（x-2）2+y2=1．
设P（x，y），则
=(x-2，y)，CP
=(x，y)，OP
所以
•CP
=x(x-2)+y2=x2+y2-2x=2x-3.OP
因为（x-2）2+y2=1，所以（x-2）2≤1，即-1≤x-2≤1，得1≤x≤3．
所以-1≤2x-3≤3，即
•CP
的取值范围为[-1，3]．OP
When Mr. Hunt woke up in the morning, he felt his bedroom was very bright. He thought he ____ to turn off the light again. He sat up and tried to do that. And now he ____ it was the sunlight. Mr. Hunt went to see their daughter in the city two days ago. She cooked some food for him ____ he left. But Mr. Hunt hoped to have breakfast in a restaurant near the park. And then he could walk ____ the lake. He put on his clothes and went out. The sun was shining brightly in the sky and the ____ was fresh (清新的) . But people were busy and he could see only some old people and children. He went in the restaurant and sat down at a table, waiting for the ____. “Hi, Peter!” someone called him and he saw it was his ____ Richard. “Hi, Richard. Glad to meet you here.” “Glad to meet you, too,” said Richard. “I’m sorry , but I ____ my wallet at home . So could you lend fifty dollars to me, please?” “Sure, but I have only twenty five dollars in my ___.” “It doesn’t matter ,” said Richard , “ then you’ll owe(欠) me twenty-five dollars and I’ll owe you ____ dollars , too . That’ll be fair (公平的) .”
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